And after swallowing a close loss to the Miami Heat Tuesday night, the team boarded its charter plane and landed here at around 3 a.m., with a game hours away against the Washington Wizards at the Verizon Center.

There was no reason for the Celtics to win Wednesday night, given such circumstances. But Gerald Wallace saw it differently. “Nobody is expecting us to win the game,” he said. “We don’t have anything to lose.”

The Celtics played that way, loose and free, and it helped them escape with a 113-111 overtime win, snapping their season-high 10-game road-losing streak.

The win, which improved the Celtics’ record to 15-29, was all the more impressive because the Celtics held on after watching their 19-point first-half lead fade into nothing.

“Everybody was just relaxed,” said Jeff Green. “When you’ve got guys going down and Coach tells you to just go out there and play free, I think that’s what we did. That’s how we got out to the lead in the first half and that’s how we kept our composure. I think everybody just played relaxed. We’ve just got to continue to do that when guys come back.”

The Celtics stayed in it behind a season-high 39 points from Green, and a career-high 20 points from Phil Pressey, who more than filled in for Rondo, helping the Celtics win their first overtime game this season.

“We’re playing hard,” said forward Kris Humphries. “A lot of teams that have our record, that have been through the tough time that we’ve been on, when Washington got back in the game [they would] have a tough time closing it out.

“We stayed in there. We fought.”

Wallace made a driving layup with 2.5 seconds left that gave the Celtics their final lead, and the Wizards’ John Wall, who had 28 points, 11 rebounds, and 10 assists for his second career triple-double, missed a jumper at the buzzer.

The score was tied at 92, 94, and 96 late in the fourth quarter, but the most remarkable shot of the night was a 3-pointer from Green with 1:18 left that tied the score at 99.

Green, a Georgetown star who was playing on his alma mater’s home floor, made it on one foot, facing two defenders, while he was off-balance and fading out of bounds. It was one of his career-high eight 3-pointers on a career-high 16 attempts.

“My old locker is right down the hall,” he said. “I live 10 minutes from here. It’s a lot of comfort here. It’s like my second home.”

It was clear that Green felt right at home.

“It was great — in front of my family, friends. I couldn’t have scripted it better,” Green said.

Said Wallace, “I think it feels good when you sleep in your own bed. He’s at home. He slept in his own bed last night. He came in well-rested and comfortable.”

The Celtics also received a huge boost from Pressey, who made 5 of 6 from 3-point range after hitting just 6 of 38 from that distance all season entering the game.

“It feels good to finally start hitting some shots, because I know I can create for my team; it’s just my shot hasn’t been falling,” he said. “It gives me some confidence.”

The Celtics hit a season-high 15 3-pointers, and Pressey’s last one from beyond the arc gave Boston a 111-108 lead in overtime.

The Wizards tied the score when Marcin Gortat made one free throw. Then the ball went to Wallace, because, Celtics coach Brad Stevens said, “Gerald is a forceful driver.”

Indeed, Wallace drove hard right and bulled his way to the rim, where he laid the ball in while absorbing contact.

“This win just shows the fight that we have as a team,” Wallace said.

Said Stevens, “I’ve said this after a lot of losses, so I’m going to sound like a broken record, but it’s not about the result, it’s about the will and the fire to compete.”

But with the game close, and the Celtics having lost so many close games, what did Stevens tell his team before his first NBA overtime?

“Coach is interesting,” Humphries said. “He gets this smile on his face and he’s like, ‘Win the game” . . . amongst other things that he’s saying strategically. He likes those situations. I see it on his face. He’s excited and he believes in us.”

Pressey agreed, and praised Stevens’s approach for keeping the team together through its struggles.

“Coach is always telling us, did we get better?” Pressey said. “Not really worrying about the score, he just wants to know if we got better that day. The last couple games [both close losses], we got better. We weren’t even looking at the loss.

“I remember Coach telling us, this is going to be a unique year this year. I mean, how many games have we lost that we could’ve won, and we’re still [four] games out of eighth place. That’s not far at all. We just have to continue to get better every game, win or lose, and we’ll be all right.”

The Celtics started four forwards and Pressey. Chris Johnson and Vander Blue, both on 10-day contracts — with Blue signing Wednesday — also played valuable minutes.

Johnson scored 9 points off the bench and Blue added a basket in his Celtics debut.

“It always happens like this,” Humphries said. “You’re down a bunch of guys, new guys [join] the team, and we finally get the win.”

The Celtics needed it, but it wasn’t to be expected on a night when so much was against them, when they were short players and energy, and on the road, where they struggle.